Quantized Filter Analysis - Introduction to Digital Signal Processing and Filter Design - page 360

the first icon on the left-hand bar in the dialog box and adding the frequency
specifications for the new filter.
7.3 QUANTIZED FILTER ANALYSIS
When we have finished the analysis of the reference filter, we can move to
construct the quantized filter as an object, by clicking the last icon on the bar
above the Analysis area and the second icon on the left-hand bar, which sets
the quantization parameters. The panel below the Analysis area now changes
as shown in Figure 7.1b. We can construct three objects inside the FDA Tool:
qfilt , qfft ,and quantizer . Each of them has several properties, and these
properties have values, which may be strings or numerical values. Currently
we use the objects qfilt and quantizer to analyze the performance of the
reference filter when it is quantized. When we click the Turn Quantization
On button and the Set Quantization Parameters icon, we can choose the
quantization parameters for the coefficients of the filter. Quantization of the filter
coefficients alone are sufficient for finding the finite wordlength effect on the
magnitude response, phase response, and group delay response of the quantized
filter, which for comparison with the response of the reference filter displayed
in the Analysis area. Quantization of the other data listed below are necessary
when we have to filter an input signal:
• The input signal
• The output signal
• The multiplicand: the value of the signal that is multiplied by the multiplier.
• The product of the multiplicand and the multiplier constant
• The output signal
The object quantizer is used to convert each of these data, and this object has
four properties: Mode, Round Mode, Overflow mode ,and Format .Inorderto
understand the values of these properties, it is necessary to review and understand
the binary representation of numbers and the different results of adding them and
multiplying them. These will be discussed next.
7.4 BINARY NUMBERS AND ARITHMETIC
Numbers representing the values of the signal, the coefficients of both the filter
and the difference equation or the recursive algorithm and other properties cor-
responding to the structure for the filter are represented in binary form. They are
based on the radix of 2 and therefore consist of only two binary digits, 0 and 1,
which are more commonly known as bits , just as the decimal numbers based on a
radix of 10 have 10 decimal numbers from 0 to 9. Placement of the bits in a string
determines the binary number as illustrated by the example x 2 = 1001 1010,